A note on the Wang-Zhang and Schwarz inequalities
DOI:
https://doi.org/10.24193/subbmath.2018.3.10Keywords:
Schwarz inequality, inner products, inequalities for sums.Abstract
In this note we show that the Wang-Zhang inequality can be naturally applied to obtain an elegant reverse for the classical Schwarz inequality in complex inner product spaces.
Mathematics Subject Classification (2010): 46C05, 26D15.
References
Diaz, J.B., Metcalf, F.T., Stronger forms of a class of inequalities of G. P´olya-G. Szeg¨o and L.V. Kantorovich, Bull. Amer. Math. Soc., 69(1963), 415-418.
Dragomir, S.S., Some Gru¨ss type inequalities in inner product spaces, J. Inequal. Pure Appl. Math., 4(2003), No. 2, Article 42, 10 pp.
Dragomir, S.S., Advances in Inequalities of the Schwarz, Gru¨ss and Bessel Type in Inner Product Spaces, Nova Science Publishers, Inc., Hauppauge, NY, 2005. viii+249 pp.
Izumino, S., Peˇcari´c, J., A weighted version of Ozeki’s inequality, Sci. Math. Japonicae, 56(2002), no. 3, 511-526.
Kre˘ın, M.K., Angular localization of the spectrum of a multiplicative integral in a Hilbert space, Funct. Anal. Appl., 3(1969), 89–90.
Lin, M., Remarks on Kre˘ın’s inequality, The Math. Intelligencer, 34(2012), no. 1, 3-4. [7] P´olya, G., Szego¨, G., Problems and Theorems in Analysis, Volume 1: Series, Integral Calculus, Theory of Functions (in English), translated from german by D. Aeppli, corrected printing of the revised translation of the fourth German edition, Springer Verlag, New York, 1972.
Shisha, O., Mond, B., Bounds on Differences of Means, Inequalities, Academic Press Inc., New York, 1967, pp. 293-308.
Wang, B., Zhang, F., A trace inequality for unitary matrices, Amer. Math. Monthly, 101(1994), 453–455.
Watson, G.S., Alpargu, G., Styan, G.P.H., Some comments on six inequalities associated with the inefficiency of ordinary least squares with one regressor, Linear Algebra and its Appl., 264(1997), 13-54.
Zhang, F., Matrix Theory: Basic Results and Techniques, Springer-Verlag, New York, 2011
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2018 Studia Universitatis Babeș-Bolyai Mathematica
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
